thnx +tan3x=2tan2x find general solution. Please give me ans.Please give me ans
Pradeep Gupta , 4 Years ago
Grade 12th pass
Trigonometry> thnx +tan3x=2tan2x find general solution....
2 AnswersVikas TU
Last Activity: 4 Years ago
tan x + tan 2x = tan 3x
Now let us simplify, tan x + tan 2x = tan 3x
tan x + tan 2x – tan 3x = 0
tan x + tan 2x – tan (x + 2x) = 0
On using the formula, tan (A+B) = [tan A + tan B] / [1 – tan A tan B]
Therefore, tan x + tan 2x – [[tan x + tan 2x]/[1- tan x tan 2x]] = 0
(tan x + tan 2x) (1 – 1/(1- tan x tan 2x)) = 0
(tan x + tan 2x) ([– tan x tan 2x] / [1 – tan x tan 2x]) = 0
Now, (tan x + tan 2x) = 0 or ([– tan x tan 2x] / [1 – tan x tan 2x]) = 0
(tan x + tan 2x) = 0 or [– tan x tan 2x] = 0 tan x = tan (-2x) or -tan x tan 2x = 0
tan x = tan (-2x) or 2tan2 x / (1 – tan2 x) = 0
[Using, tan 2x = 2 tan x / 1-tan2 x] x = nπ + (-2x)
or
x = mπ + 0 3x = nπ
or
x = mπ x = nπ/3 or x = mπ
∴ the general solution is x = nπ/3 or mπ,
Pradeep Gupta
Last Activity: 4 Years ago
tanx + tan 3x = 2tan 2x
tanx + tan3x = tan2x +tan2x
thnx - tan2x = tan2x - tan3x
tam 2x -tanx =tan 3x - tan2x
tan( 2x-x )( 1 + tan2x tanx ) = tan(3x-2x) ( 1 + tan 3x tan2x)
tanx ( 1+ tan2x tanx ) - tanx ( 1+tan3xtan2x)=0
tanx {1 + tan2xtanx -1-tan3xtan2x}=0
tanx (tan2xtanx- tan3xtan2x)=0
tanx tan2x( tanx -tan3x) =0
If tanx = 0 or tan2x = 0
x = nπ. tan2x = nπ
x=nπ/2
and tanx - tan3x =0
tanx = tan3x
tan3x = tanx
3x = nπ +x
2x= nπ
x = nπ /2
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on Trigonometry
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
Trigonometry
1 Answer Available
Last Activity: 2 Year ago(s)
\tFind the general solution of equation tan3∂=cot2∂For all angles between -720 and +720
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)